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Lecture19

# Lecture19 - STAT 350 Lecture 19 8.2 Tests Concerning...

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STAT 350 Lecture 19 8.2 Tests Concerning Hypotheses About Means

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8.2 Tests Concerning Hypotheses About Means Review: One-Sample z Test for population mean One-Sample z Test for population proportion One-sample t Test Two-sample t Test Tests with paired data
One-sample z Test for a single Mean: General Setting: X 1 , ., X n : SRS require large sample size n no requirement on population distribution μ is the unknown parameter of interest The null hypothesis is H 0 : μ = μ 0 The alternative hypothesis could be: H a : μ ≠ μ 0 (two-sided) H a : μ > μ 0 (one-sided) H a : μ < μ 0 (one-sided)

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Test Statistic for population mean (large sample) For population mean : Notes: Measures compatibility between H0 and data n s X z 0
One-sided vs. two-sided If, based on previous data or experience, we expect increase , more , better , etc. ( decrease , less , worse , resp.), then we can use a one sided test. Otherwise, by default, we use two-sided. Key words: different , departures , changed ”…

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Setting up Hypotheses If an investigator wishes to demonstrate conclusively that a particular assertion is correct, or wants to see strong evidence for an assertion before taking action, that assertion should be incorporated in H a Please read page 346 in your textbook
One-sample z Test for population proportion: General Setting: X 1 , ., X n : SRS require large sample size n population distribution: Bernoulli (0 or 1) with population proportion π π is the unknown parameter of interest The null hypothesis is H 0 : p = π 0 The alternative hypothesis could be: H a : p π 0 (two-sided) H a : p > π 0 (one-sided) H a : p < π 0 (one-sided)

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